A piece of wire of total length L units is used to form the nine edges
of a prism whose ends are equilateral triangles and whose other faces
are rectangles. What is the maximum surface area of this prism?

How many ways are there to make dice out of the Platonic solids (i.e. 4,
6, 8, 12, and 20 sides)? How many of those ways have opposite face sums
equal? What would the opposing face sums be for each type?

Calculate the orders of the following groups of rotations: of a
regular tetrahedron, a regular octahedron, a regular dodecahedron, and
a regular icosahedron. I'm having trouble figuring out the
stabilizers. I know that the order of the group of rotations is equal
to the order of the orbit times the order of the stabilizer.